SWS - Sequential Winner Salvation (More monotonic IRV)

Procedure to find the loser, usable in Sequential Loser Elimination methods.


  • The votes are normalized (normalization as desired).
  • The normalized votes are aggregated (usually with the sum), and the best candidate (highest sum) is removed from the votes, or “saved”.

This process is repeated several times, until there is only one candidate left who will be the loser (to eliminate in SLE).

SWLE: SLE method that uses SWS to find the loser is called Sequential Winner-Loser Elimination.

Use votes with ranges (converted then in ranking), in which candidates can have the same position.


  1. The votes are normalized with B-Max Norm (greater value to 1, the others to 0), and the candidate with the highest sum of points is removed (saved) from the votes.
  2. Procedure 1 is repeated until only 1 candidate remains. The remaining candidate is eliminated, and those removed (saved) in procedure 1 are added again.
  3. By repeating steps 1 and 2, one candidate is eliminated each time and in the end there will only be one left, the winner.

In practice it’s the IRV that accepts candidates with the same rating, and on which the SWS method is used.

You can test this system on this Codepen.

W-IRRV (variant)
It’s W-IRV with the following extra rule:

  • the weight of the vote is halved every time one of the candidates supported by the vote (in 1st position) is saved. The weight of the votes is restored after finding the loser.

I called this procedure SWS for convenience; if there is already one similar (or the same :sweat_smile:) let me know.

This is not monotonic.

29: A>D>B>C
6: A>B>C>D
25: B>C>D>A
14: C>B>A>D
6: C>B>D>A
10: D>A>B>C
10: D>C>A>B

A X 55* 45 49
B 45 X 70* 51*
C 55* 30 X 51*
D 51* 49 49 X

  1. Protect A, then D. B beats C.
    B31 C20 D49

Now the preferences are A35, B45, D20
Protect B
D beats A

Final round:
B beats D.

29: A>B>D>C
6: A>B>C>D
25: B>C>D>A
14: C>B>A>D
6: C>B>D>A
10: D>A>B>C
10: D>C>A>B

A is protected, then B is protected. C beats D.

A is protected.
B beats C.

Final round: A beats B.

You’re right, I correct it. Great example.
It satisfies the monotony only in case there is a Condorcet winner.

I added the variant W-IRRV which seems more sensible to me and which does not fail the monotony in the example you have proposed (but probably fails in some other case).

(I’m assuming you’re referring to only the votes for the protected candidate.)

If you do this, the method is no longer Condorcet, since the elimination round is no longer a normal pairwise matchup, but a weighted one.

Now I have specified better (you got it right).

Yes, W-IRRV isn’t Condorcet but my main focus with this system was resistance to tactical votes.